if a superliminal object did exist, would it appear as two identical objects to us

[CPL.Luke]

this is a continuation of a discussion that started in the thread faster than light -ve. The discussion seemed interesting enough to warrant a new thread and seemed to be heading in the direction of a proper scientific discussion, and so I created the thread here.

 

Mowgli said that he had worked out some math showing what a superluminal object would look like to us. It sounded interesting so lets see it.

 

although for simplicities sake lets consider a point first and then move onto

[Mowgli]

Okay, I will start with an animation first to make it interesting. I will post the notations and algebra in the next post.

 

In the figure below, we have a (purely hypothetical) superluminal object - the white circle flying across the animation at ten times the speed of light. As it flies by, it emits light. We consider the light rays (the red lines with small red circles at the end) coming towards the observer at the bottom-center of the animation. As we can see, the first ray of light that reaches the observer is emitted at a point close to the point of closest approach to the observer, indicated by a black dot that appears when the ray reaches him, say at time=[math]t_o[/math]. The rays emitted before this first ray reach the observer after [math]t_o[/math]. This reversal of the order in which the rays reach the observer gives rise to the perception of two objects moving away from the black dot. (If the object doesn't change during its flight, the two "phantom" objects are identical to each other.)

 

 

Now, my question is, if we see two objects in a symmetric formation in the night sky, can we be sure that they are really two, and not our perception of one object in motion? Of course we can if we say that nothing can really travel faster than light. Assuming hypothetically that we didn't know about SR and its constraint on the speed, is there any way we could work out the "real" speed from our observation of the rate of angular separation? My feeling is that there are at least two configurations (one superluminal object going in one direction or two objects - superluminal or otherwise - going in opposite directions) which will result in the same observation.

[Mowgli]

This post gives the algebra behind the animation. First, let's define the notations used using the following figure.

 

 

Here, the object is traveling along the thick horizontal line at a speed [math]\beta[/math]. The black dot in the animation (where the object first appears to the observer) is B'. B is the point of closest approach. Let's set the time [math]t=0[/math] when the object is at the point B. The line of flight (at its closest point B) is at a distance of y from the observer at O. A is a typical point at a distance x from B. [math]\theta[/math] is the angle between the line of flight and the observer's line of sight. [math]\phi[/math] is that the angle that the object subtends at the observer's position O with respect to the normal. Let's set [math]c=1[/math] to simplify the algebra, so that [math]t_o[/math], the observer's time is [math]t - y[/math]. (A- is another representative point where [math]t, x[/math] and [math]\phi[/math] are negative.)

 

With these notations, we can write down the following equation for the real position of the object at time [math]t[/math]:

 

[math]

x = y\tan\phi = \beta t

[/math]

 

Or,

[math]

t = \frac{y\tan\phi}{\beta}

[/math]

 

A photon emitted by the object at A (at time [math]t[/math]) will reach O after traversing the hypotenuse. A photon emitted at B will reach the observer at [math]t = y[/math], since we have chosen [math]c = 1[/math]. We have defined the observer's time [math]t_o[/math] such that [math]t = t_o + y[/math], then we have:

 

[math]

t_o = t + \frac{y}{\cos\phi} - y

[/math]

 

which gives the relation between [math]t_o[/math] and [math]\phi[/math].

 

[math]

t_o = y\left( \frac{\tan\phi}\beta + \frac{1}{\cos\phi} - 1\right)

[/math]

 

Expanding the equation for [math]t_o[/math] to second order, we get:

 

[math]

t_o = y\left(\frac\phi\beta + \frac{\phi^2}{2}\right)

[/math]

(Call this equation Q.)

 

The minimum value of [math]t_o[/math] occurs at [math]\phi_{0}=-1/\beta[/math] (which defines the position of the black dot in the animation, the point B') and it is [math]{t_o}_{min} = -y/2\beta^2[/math]. To the observer, the object first appears at the position [math]\phi=-1/\beta[/math]. Then it appears to stretch and split, rapidly at first, and slowing down later.

 

The quadratic equation Q above can be recast as:

[math]

1+\frac{2\beta^2}{y}t_o = \left(1+\beta\phi\right)^2

[/math]

which will be more useful later in the derivation. (Call this equation U.)

 

The angular separation between the objects flying away from each otheris the difference between the roots of the quadratic equation Q:

 

[math]

\Phi \,=\, \phi_1-\phi_2 [/math]

[math]

\,=\, \frac{2}{\beta}\sqrt{1+\frac{2\beta^2}{y}t_o} [/math]

[math]

\,=\, \frac{2}{\beta}\left(1+\beta\phi\right)

[/math]

making use of the ``useful'' equation U above. Thus, we have the angular separation either in terms of the observer's time ([math]\Phi(t_o)[/math]) or the angular position of the object ([math]\Phi(\phi)[/math]) as illustrated in the next figure, which illustrates how the angular separation is expressed either in terms of the observer's time ([math]\Phi(t_o)[/math]) or the angular position of the object ([math]\Phi(\phi)[/math]).

 

 

The rate at which the angular separation occurs is:

 

[math]

\frac{d\Phi}{dt_o} \,=\, \frac{2\beta}{y\sqrt{1+\frac{2\beta^2}{y}t_o}}

[/math]

[math]

\,=\, \frac{2\beta}{y\left(1+\beta\phi\right)}

[/math]

 

Again, making use of the useful equation U. Defining the apparent age of the formation [math] t_{age} = t_o - {t_o}_{min}[/math] and knowing [math]{t_o}_{min} = -y/2\beta^2[/math], we can write:

 

[math]

\frac{d\Phi}{dt_o} \,=\, \frac{2\beta}{y\sqrt{1+\frac{2\beta^2}{y}t_o}}[/math]

[math]

\,=\, \frac{2\beta}{y\sqrt{1-\frac{t_o}{{t_o}_{min}}}}[/math]

[math]

\,=\, \sqrt{\frac{4\beta^2}{y^2}\,\times\,\frac{-{t_o}_{min}}{t_o-{t_o}_{min}}}[/math]

[math]

\,=\,\sqrt{\frac{2}{y\, t_{age}}}

[/math]

 

Note that in order to go from the angular rate to the speed (even the apparent speed), we need to estimate [math]y[/math], which is model-based.

 

Now, can you tell me why the object doesn't appear at two places if [math]\beta < 1 [/math]?

[Severian]

This is a fairly well known phenomenon for the sound emitted by supersonic aircraft.

[CPL.Luke]

Mowgli it appears in the animation as if the two "image" dots are still moving with superluminal velocity, this would seem to give a mechanism for determining whether an two identical images in the sky are from 1 superluminal object or from gravitational lensing etc.

[Anjruu]

It seems to me that this is a sonic boom, but in light. A visible boom, then. The algebra and functions behind it should be fairly similar if not identical, substituting in c instead of the speed of sound. Is this correct?

[Mowgli]

It seems to me that this is a sonic boom, but in light. A visible boom, then. The algebra and functions behind it should be fairly similar if not identical, substituting in c instead of the speed of sound. Is this correct?

It is a "luminal" boom, as shown in the attached picture, which is another way of looking at the animation. In this picture, the circles represent the wave that the moving object (say the first peaks) emits. What is also of interest is how the frequency as measured at O changes. It starts at infinity and rapidly decreases. In fact, in the animation in the previous post, the color of the "phantom" objects is supposed to represent their redshift as seen by the observer, although it is not done to scale. I didn't post the algebra behind it yet, but the spectrum and its time evlution predicted in this "luminal" boom can explain GRBs with remarkable simplicity. (Except, of course, that the explanation violates Lorentz invariance.)

 

[Mowgli]

Mowgli it appears in the animation as if the two "image" dots are still moving with superluminal velocity, this would seem to give a mechanism for determining whether an two identical images in the sky are from 1 superluminal object or from gravitational lensing etc.

We can measure only the angular speed. In order to translate that to a linear speed measurement, we need to estimate the distance to the line of flight y. This estimate is model dependent, and is always done in such a way that the real speed is subluminal and the phantoms are in fact two distinct objects. It can be shown that as long as the angular rates are not identical, one can always find a distance y to the system such that the real speed (of an assumed symmetric back to back ejection) is subluminal, even if one of the sides may have apparent superluminal speed. This is indeed how they calculate the upper limit on the distance y in astrophysics, by enforcing Lorentz invariance. I can show you proof if you like.

 

I was thinking more in terms of radio sources (like Cygnus A, as attached) and their spectra rather than gravitational lensing. If I remember right, the jet to the right of the core (the tiny red dot at the center) is a nearly continuous and collemated "ejecta" of over 5000 light years, which implies long memory or coordination over great distances. (Or, was it in M87?)

 

[Severian]

But the objects would need to be completely identical. These are not.

[Mowgli]

But the objects would need to be completely identical. These are not.

Actually, the "phantom" objects will be identical only if the superluminal object doesn't change during its flight. In my second post with the algebra, if you look at the first figure, let's say the light rays from A- and A reach the observer at the same instant in time, giving him the impression that he is seeing two objects. In "reality," he is seeing the object as it was at two different instants in time, say t- and t. During the time interval between t- and t, the object may have changed. So you can expect only a rough symmetry.

 

In fact, I was a little concerned about CPL's use of the word "identical" in the thread title, so I put a disclaimer in my first post stating: "(If the object doesn't change during its flight, the two "phantom" objects are identical to each other.)"

[rajama]

... the "phantom" objects will be identical only if the superluminal object doesn't change during its flight. In my second post with the algebra, if you look at the first figure, let's say the light rays from A- and A reach the observer at the same instant in time, giving him the impression that he is seeing two objects..."

 

Neat.

 

So a continuous object would appear reflected about the origin, but not top to bottom... doesn’t gravitational lensing reflect top to bottom?

[Mowgli]

Neat.

 

So a continuous object would appear reflected about the origin' date=' but not top to bottom... doesn’t gravitational lensing reflect top to bottom? [/quote']

I'm not very sure of gravitational lensing. It never occurred to me to think of them as possible perceptual effects. But you are right, a continuous object (or a group of objects moving together) should appear as a reflection about a so-called core because of the way we perceive superluminality.

 

There is a significant number of such objects, see the DRAGN atlas. The assosicated pages at this Web site give you a good overview of the current model for DRAGN's (Double Radiosources Associated with Galactic Nucleus). As the name indicates, the spectra of these objects are in the RF region. Why is that? Looking at such double-lobed structures as the way we (or our radio telescopes) would see superluminal motion also gives a compellingly simple explanation for the spectra. In a sonic boom, the frequency (as a function of time) as heard by the observer asymptotically tends to zero, whatever be the frequency emitted. So, we could think of DRAGN's as an aftermath of luminal booms.

 

The other side of the boom (the leading edge where the frequency is infinite) holds an explantion for Gamma Ray Bursts (GRB's). Thus, we could unify these two seemingly different astrophysical phenomena using one model. The trouble, of course, is that the model violates Lorentz invariance. I know now that it will never be taken seriously unless I can come up with a complete theory that will explain everything that SR can explain. Anybody interested in taking on that task with me?

 

This difficulty notwithstanding, I have done some detailed comparisons with the existing data on the time evolution of the spectra and made some predictions about the features, including what observations will invalidate this model. If anybody is interested, I can post the article or a link to it.

[Mowgli]

Since this thread has been idle for a while, I thought I would some other ideas related to it. I would really like to hear from the resident experts, if they have any comments, criticism or any other kind of feedback or suggestions.

 

In thinking about the hypothetical superluminal object, one may rightly criticize that there is no point in discussing it; after all, nothing is supposed to travel faster than light. That brings us to the basic question -- what is so important about light that it should figure in the basic structure of space and time?

 

In order to understand the importance of light in our space and time, let's consider a different space-time -- for instance, one created by echolocation. It's not difficult to work out how the (blind) bat would perceive moving bodies. It turns out that the bat will think that nothing can move faster than the speed of sound. (A supersonic object moving away from the bat can never be sensed because the sound the bat emits will never reach the object, and there will be no reflection. An approaching supersonic object will pass the bat before the reflected sound reaches it, and will become a receding object.) It can also be shown that there will be a time dilation and length contraction in echolocation as predicted in special relativity (SR), again with the speed of light replaced with that of sound. Now, if the bat were intelligent enough to theorize about space and time, the theory it would have come up with would have been uncannily similar to SR with the speed of light replaced with that of sound. In this case, we can clearly see that the bat is making a theory about its perceived reality because we know what the underlying absolute reality is -- it is the reality as we (humans) sense it using a faster mode (light).

 

It stands to reason that our space-time also must have perceptual effects. We can either attribute the effect that the finite speed of light has in our perception of moving bodies to the properties of space and time (as in SR), or we can try to "take them out" from our perception of motion. It turns out that we cannot take them out because multiple configurations can result in the same perception; it is an ill-posed problem with many valid solutions. The next best thing we can do (that I could think of) was to work forward; ie, guess a configuration and work out how we would perceive it, much like I did in the case of echolocation. I considered a hypothetical superluminal object and worked out in detail what our perception of it would be. The "luminal boom" it creates explains neatly many of the puzzling features of a Gamma Ray Burst (GRB) including the time evolution of the afterglow. The aftermath of the luminal boom (asymptotically low frequencies) explains the spectra, the observed symmetry and other time/angle dependent features of radio sources (DRAGNs). I made some predictions about their kinematics, verified some of them with existing data. I also provided some other predictions, which, if observed, will falsify my model. (Because if a model cannot be falsified, it's no model at all.) For instance, a clear movement in the angular position of the core of a DRAGN (which would be the position of the so-called host galaxy) would invalidate my model. Or, the appearance of a superluminal "knot" in one of the jets with no counterpart in the opposing jet will also prove that my model is wrong. I can point you to my article (which I optimistically called a journal article) if you are interested in the technical details.

 

Despite the success of my model in describing these phenomena, it is still a tough sell because the current belief is that SR applies to the absolute reality. In other words, once you take out the light travel time (LT) effects that I described in the preceding paragraph, what is left is the space-time that is assumed to obey SR. (Actually, one of the experts in this forum said that to me earlier.) It is an understandable assumption because, frankly, the LT effects are not that hard to work out, and it is not conceivable that the great minds of the last century didn't work them out and see their implications. The only explanation I can think of is that they were kind of blinded by the assumption that our perceived reality was the absolute reality, and that their theories applied to the absolute reality. (Is this one way of describing scientific realism?) The real point that I'm trying to make is that SR applies to our phenomenal reality, not to its noumenal causes. This is a philosophical stance, and physics journals are not ready (perhaps rightly) to just take my word for it

 

Looking at it philosophically, one can say that there is a noumenal reality of which our phenomenal perception is all based on light. Furthermore, our cognitive model for the phenomenal reality is space. Space is a cognitive representation of the photons falling on our retina, much like sound is a representation of pressure waves in the air, temperature is a model for molecular movements and smell is a model for chemical concentrations. We cannot imagine space to be a model only because we have no "higher" sense modality, and a consequent model, to understand it, which we did in the case of sound, smell and temperature. Given that space is created out of light input, it becomes immediately obvious why the speed of light is a fundamental property of our perception of space. So clearly, light and its speed are the most important things in our reality. What do you think?

 

There is quite a bit more to it than what I can post here (related to neuroscience, evolutionary biology, etc.); after all, I wrote a full-length book about it...

[Severian]

In thinking about the hypothetical superluminal object' date=' one may rightly criticize that there is no point in discussing it; after all, nothing is supposed to travel faster than light. That brings us to the basic question -- what is so important about light that it should figure in the basic structure of space and time?

[/quote']

 

To be honest, although it is a nice idea, that was my objection. The important property of light is that it has no mass. Any other particle with no mass also travels at the limiting velocity and it is really just coincidental that we call it the 'speed of light'. In fact, I have always thought it was a mistake that physicists call it the 'speed of light' - 'limiting speed' would have been a much better term.

 

This objection is hard to get around. We are alble to produce particles in the lab which travel near c and their dynamics perfectly meshes with SR. We have never seen anything travelling faster and never mind how much energy we pump into them, we cannot get massive particles up to c. It is not so much the limit v<c that is the test of SR, but the relation between the energy and velocity (really momentum) and that has been very well tested now.

 

If particles really did travel at speeds >c why do we not see your two identical objects in our particle physics experiments? I have been trying to think about this in the context of matter-antimatter, but haven't really got my head round it yet. One could imagine that the electron and positron produced in pairs were like this. I worried to start with that the positron and electron have opposite quantum numbers (eg charge) so they are not identical, but since the light from the positron would be coming at us in the 'wrong order' it would actually appear that way naturally in your set-up. (In QFT positrons are identical to electrons travelling backwards in time.) My real problem in thinking about this on a subatomic level is that the emission of light actually effects the particle so much that the simple picture you presented is invalid. I need to think some more.

 

On the other hand, from a particle physics point of view, SR predicts everything absolutely correctly, so why should I even look fro another model? Indeed, isn't the non-universality of the time co-ordinate a reasonable thing to expect on the mathematical level if we were not blinded by our everyday life experiences?

 

In order to understand the importance of light in our space and time, let's consider a different space-time -- for instance, one created by echolocation. It's not difficult to work out how the (blind) bat would perceive moving bodies.

 

Although I take you point, this is a wee bit bogus though because the bat can (I presume?) also hear sounds which something else emits. So a bat would still hear a supersonic jet passing overhead - it just cannot use its sonar to detect it. We don't emit the light we use to see so we are phenomenologically very different from a bat.

[Mowgli]

To be honest' date=' although it is a nice idea, that was my objection. The important property of light is that it has no mass. Any other particle with no mass also travels at the limiting velocity.

<snip>

This objection is hard to get around. We are alble to produce particles in the lab which travel near c and their dynamics perfectly meshes with SR. We have never seen anything travelling faster and never mind how much energy we pump into them, we cannot get massive particles up to c. It is not so much the limit v<c that is the test of SR, but the relation between the energy and velocity (really momentum) and that has been very well tested now.

[/quote']

Thanks, Severian, for taking the time to post a long and considered reply.

 

Yes, the verification of SR in HEP is hard to explain away. I don't have all the answers, but I can give you a few pointers to kindle your skepticism.

• The fact that we cannot accelerate particles beyond the speed of light shouldn't be a surprise, given that the way we accelerate them is by having them ride an RF wave. By increasing the energy input, we presumably increase the amplitude of the RF wave, not the speed. This will have the effect of the particles being better bunched, but you cannot accelerate them beyond c this way.
  
• Many have reported negative neutrino mass squared measurements, which strongly suggests that neutrinos should have superluminal speed. If I remember right, it was a spectrum end-point kind of measurement that is hard to misinterpret.
  
• Even though we have accepted it, all massless particles traveling at the speed of light (or the limiting speed) is basically an assumption. Wasn't there a PRA paper by Tom Van Flandern indicating that the speed of gravity had to be superluminal in order to have stable orbits?
  

I have been trying to think about this in the context of matter-antimatter' date=' but haven't really got my head round it yet.

<snip>

I need to think some more.

[/quote']

I toyed with this idea a bit, mainly inspired by the fact that anti-particles are particles traveling backward in time in Feynman diagrams, as you pointed out. I thought the notion of anti-particles being superluminal particles would be a stretch. A particle physicist myself, I could not quite imagine how you would have e+e- collisions that way. I'm glad that you are thinking about it seriously. Please post if you can figure it out.

On the other hand' date=' from a particle physics point of view, SR predicts everything absolutely correctly, so why should I even look fro another model?

[/quote']

HEP phenomenology is built on SR. So the agreement may be built in.

Indeed' date=' isn't the non-universality of the time co-ordinate a reasonable thing to expect on the mathematical level if we were not blinded by our everyday life experiences?

[/quote']

Well, that depends on what time really is. If one thinks of time as something similar to a spatial coordinate, sure, one doesn't expect it to be universal. On the other hand, if one thinks of it as a mathematical construct to keep track of the order of events, one does expect it to be universal.

Although I take you point' date=' this is a wee bit bogus though because the bat can (I presume?) also hear sounds which something else emits. So a bat would still hear a supersonic jet passing overhead - it just cannot use its sonar to detect it. We don't emit the light we use to see so we are phenomenologically very different from a bat.[/quote']

This little paragraph has so many points to respond to!

• As you pointed out earlier, the way a bat would hear a supersonic jet passing overhead is exactly what my original animation was. Here, there is an implicit definition of simultaneity -- if the light rays (or the sound) from two events reach the observer at the same time, the events are simultaneous. In fact, this is the basis of my model for the kinematics and spectra of GRBs and DRAGNs.
  
• It so happens that a sonar-like sensory mechanism is quite similar to the definition of simultaneity in SR (equal light travel time back and forth). The reason why speed always appears as [math]\beta^2[/math] in SR is this definition, giving it the symmetry (and the twin paradox, and almost all these time dilation thought-experiments we have been posting here).
  
• Due to this similarity, if I were to work out bats' perception of motion, I'm pretty certain that it would be SR, although I haven't done it. If I can find enough time after my day job, I will try this sometime. What I did work out was the algebra behind the animation. The resulting equations are odd in [math]\beta[/math], giving a natural resolution to the twin paradox.
  

[Severian]

• The fact that we cannot accelerate particles beyond the speed of light shouldn't be a surprise' date=' given that the way we accelerate them is by having them ride an RF wave. By increasing the energy input, we presumably increase the amplitude of the RF wave, not the speed. This will have the effect of the particles being better bunched, but you cannot accelerate them beyond c this way.[/list']

 
That's not quite what I meant though. I mean that when two particles interact, in principal one could imagine them getting enough of a kick to go superluminal. This doesn't happen because the momentum conservation is always 4-momentum in the SR sense. (This is why I said that the real objection isn't really the <c bit but the way we add momenta.)
 

• Many have reported negative neutrino mass squared measurements, which strongly suggests that neutrinos should have superluminal speed. If I remember right, it was a spectrum end-point kind of measurement that is hard to misinterpret.

 

This is a slightly different reason though. The endpoints fall at a specific (non-zero) mass value for zero neutrino masses, and the deviation from this provides the neutrino mass squared). However the position of the endpoint is of order a GeV² (it is a baryonic mass scale since it is beta decay) while the neutrino mass is order (0.01eV)², so you have to measure the endpoint very accurately. In principle, your error measurements will be gaussian and if the error is large enough you will sometimes get the neutrino deviation going the wrong way, giving a negative mass-squared. In other words it is due to the extreme difficulty in measureing such a small quantity.

 

(Unless of course this is a different experiment which which I am not aware.)

 

• Even though we have accepted it, all massless particles traveling at the speed of light (or the limiting speed) is basically an assumption. Wasn't there a PRA paper by Tom Van Flandern indicating that the speed of gravity had to be superluminal in order to have stable orbits?

 

I presume you are refering to this (I am not sure you can access this outside a university?)

 

I am not familiar with this paper at all, so wouldn't like to comment. I will print it off and take a look.

 

I toyed with this idea a bit, mainly inspired by the fact that anti-particles are particles traveling backward in time in Feynman diagrams, as you pointed out. I thought the notion of anti-particles being superluminal particles would be a stretch. A particle physicist myself, I could not quite imagine how you would have e+e- collisions that way. I'm glad that you are thinking about it seriously. Please post if you can figure it out.

 

Yes, that occured to me too. You really need a mechanism for doing the exact opposite of your animation, ie. you need the light from the far away ends getting to you first.

 

HEP phenomenology is built on SR. So the agreement may be built in.

 

That is not entirely fair. HEP has made quite a few predictions which didn't have to be true. For example if SR was wrong would we have been able to correctly measure the W and Z mass and have them agree with the theory? (The theory which assumes SR would have predicted the same ratio, but I don't think the assumption of SR in the data taking would necessarily have agreed.)

 

Well, that depends on what time really is. If one thinks of time as something similar to a spatial coordinate, sure, one doesn't expect it to be universal. On the other hand, if one thinks of it as a mathematical construct to keep track of the order of events, one does expect it to be universal.

 

In SR it is both, but the second property doesn't require it to be universal - only the ordering of different times has to remain the same.

 

• It so happens that a sonar-like sensory mechanism is quite similar to the definition of simultaneity in SR (equal light travel time back and forth). The reason why speed always appears as [math]\beta^2[/math] in SR is this definition, giving it the symmetry (and the twin paradox, and almost all these time dilation thought-experiments we have been posting here).

 

If I think about my derivation of time dilation in my lectures to first year undergrads I can see exactly why this is. In the thought experiment one measures distance by firing a laser from the observer to the object and recording how long it takes. Clearly this parallels sonar.

 

• Due to this similarity, if I were to work out bats' perception of motion, I'm pretty certain that it would be SR, although I haven't done it. If I can find enough time after my day job, I will try this sometime. What I did work out was the algebra behind the animation. The resulting equations are odd in [math]\beta[/math], giving a natural resolution to the twin paradox.

 

This bit I am not so convinced about because the reason SR somes about is because of the assumption of universality of c in all frames. I suspect you will have to change your light/sound speed for the different frame and thus get a different answer. I haven't done the (non SR) calculation either though...

[Mowgli]

This doesn't happen because the momentum conservation is always 4-momentum in the SR sense.

Yes, the invariant mass is a tough nut to crack. I thought about it for a while, and could not find a real chink there. I have a notion that the concept is sufficiently cyclic that it is self-consistent. I wanted to write a small simulation to illustrate this, and will do it when I have some time. (Take a particular decay, say D to Kpi, assume the daughter momenta to be well measured, assume some other daughter masses, and consequently their energies, and estimate the width of the D peak.) I have to admit though that I'm not very hopeful that I will be able to prove my point. (Why would the particle misidentification - switch the Kaon and pion, I mean - broaden the D peak?) This is one of the things I may not be able to explain away easily.

 

About neutrino mass squared, looking at the papers again, I see that the measurements are like -2 +- 3 eV², quite consistent with zero.

 

As an aside related to this, I read this little story about standards of evidence and the need to examine our biases. Imagine that a study done on tooth decay and smoking, and a significant correlation is found between them. Assume that eighty percent of smokers are found to have bad teeth, while only forty percent of non-smokers have bad teeth. Based on this, it is concluded that one of the ways of avoiding bad teeth is not to smoke. When I first read this story, the conclusion sounded completely reasonable to me, until the bias was pointed out later. Did it fool you as well? It's important to identify and avoid biases in sciences especially when it may not be obvious.

 

I presume you are refering to this

 

Yes' date=' that is the paper I was referring to.

 

That is not entirely fair. HEP has made quite a few predictions which didn't have to be true. For example if SR was wrong would we have been able to correctly measure the W and Z mass and have them agree with the theory? (The theory which assumes SR would have predicted the same ratio, but I don't think the assumption of SR in the data taking would necessarily have agreed.)

 

As I mentioned earlier, my model is not (yet) a complete theory. Figuring out how thousands of very intelligent scientists consistently went wrong over a hundred years is not something I can reasonably expect to complete in my lifetime - not fair on myself.

 

Nonetheless, let me try it this way - why not take my model for its own merit in how well it explains the astrophysical phenomena, and how much simpler it is compared to the current models? Given that we use different physics (QM or SR) at different length and speed scales, we may suspend our disbelief for a while. After all, as you pointed out, my picture of how we perceive superluminality doesn't apply to particles. In fact, the subnuclear particles are not "perceived" at all, and they exist only as a result of our acceptance of scientific realism. But this is another topic altogether.

 

This bit I am not so convinced about because the reason SR somes about is because of the assumption of universality of c in all frames. I suspect you will have to change your light/sound speed for the different frame and thus get a different answer. I haven't done the (non SR) calculation either though...

 

What is required is the assumption that the speed of light/sound is independent of the source' date=' which is true for wave propagation.

 

I should come back to my main point, which is that SR applies to our perception of motion. This is more or less obvious if we look at its original derivation making use of light travel time effects. So, saying that SR applies to the space and time after we take out the light travel time effects is not consistent with its derivation. What is done afterwards in Einstein's article is an assertion that our perception [i']is[/i] the absolute reality. My argument is merely that we should be mindful of the distinction between the absolute reality and our percpetion of it. If we are, then we can find an elegant explanation for certain astrophysical and cosmological phenomena.

 

Thank you for taking my ideas seriously and spending the time and effort to think and talk about them.

[CPL.Luke]

Mowgli, I think that your idea could mesh with astronomical observations of superluminal objects. IF you assume that there is some mechanism in the universe for changing the reference frames in such a way that an object can appear to be travelling faster than the speed of light in our frame and in its own corner of the universe it could be measeared to be travelling at a sub light velocity.

 

I think this could be a possibility because you mentioned two objects that you believe are in fact one object traveling superluminally, are close to the galactic core, a place where there are some very large and complex gravitational and electromagnetic fields at work, and in my mind it is entirely possible that such a phenomena could exist.

 

 

As for the idea that the electron and positron are one particle traveling superluminally. I'm curious to see what would happen if in your animation you had two superluminal particles that either

 

A: intersect

B:collide

C: some combination there of.

 

and then plotted our observer's observation of the points, it would be intersting to see if a collision between two superluminal particles would result in us seeing the "image" particles collide.

 

 

EDIT: actually I think the core of this debate lies in how an EM wave would behave if it was observed coming off a superluminal object traveling in a straight line away from the observer, if there is a meaningful answer to this question then I would say that it is possible that there observable objects (like the ones mogli pointed out) that could be moving superluminally.

 

I say that this is the core issue because the notion of every superluminal object in the universe being oriented such that it travels like the hypothetical dots in mowgli's animation is more than a bit ludicrous, and if there is a meaningful answer to what EM waves look like when they are moving superlimunally, then we would know that there are telltale signs that an object is superluminal, and just by my own intuition if there is a meaningful answer to the question than I wouldn't doubt that the universe displays it.

[Mowgli]

I say that this is the core issue because the notion of every superluminal object in the universe being oriented such that it travels like the hypothetical dots in mowgli's animation is more than a bit ludicrous...

Acutally, the trajectory I assumed for the superluminal object is more general that it looks. Let me explain why. Imagine a superluminal object going in some random direction (but still in a straight line). This line of flight has a point of closest approach to us. What my calculation says is that we won't see it until the object is close to this point (point B' in my second post above). At this point, the observed emission of the object is in the gamma region (the luminal boom alluded to earlier). Then the spectrum quickly moves through the x-ray, visible region on to RF (which concides with what we observe in GRB afterglows). As time tends to infinity, the phantom objects are so deep in the RF region that we won't see them at all; we may see only some microwave radiation. So, whatever be the direction in which the superluminal object is moving, as long as it is moving roughly in a straight line, our perception of it is roughly similar (but with different time constants depending on the distance and the speed).

 

I didn't want to bring up this part of my speculation because it calls for even bigger leaps of faith, but now is probably a good time to do so. Let's suppose, hypothetically, that our universe is a collection of possibly superluminal objects (galaxies) moving in random directions and ask ourselves the question how we and our telescopes will observe it. It is not difficult to show that most of these objects will look as though they are receding from us close to the speed of light (as measured by their redshifts), there will be a significant amount of low frequency isotropic radiation, there will be symmetric radio sources and occassional gamma ray bursts and so on. In short, our perception will be pretty close to what we do perceive! I know this sounds far-fetched, but please remember, when I said the laser dot on the ceiling would appear at two place at the same time, that sounded quite far-fetched as well. Now, tell me, is it any wonder that I called my book The Unreal Universe?

 

One quick question to tickle your brain - if there is a superluminal explosion, how would we perceive it? For example, imagine a star explodes at say 12 light years from us, the debris is thrown around in a spherical shell that moves away from the center of the star at a constant superluminal speed of say 2c. What will we see?

[CPL.Luke]

Mowgli the problem is that if we assume that the debris from the star is emitting radiation, we would be unable to define at present what that light will look like.

 

according to the dopplar shift for an object coming towards us, the light should be shifted to an infinite frequency when the debris is coming at us at 1C let alone 2C. You can't just say that the light will have been shifted to the gamma ray range, because there are no physics to describe an observable faster than light object.

 

 

In my mind the only way that it could work would be if there was a luminal boom that behaved almost exactly like a shockwave from a sonic boom, to my knowledge no one has ever worked on what a light shock wave would look like, so once again it seems like the only way to show that a superluminal object could exist would be to define real observables.

[Mowgli]

Mowgli the problem is that if we assume that the debris from the star is emitting radiation' date=' we would be unable to define at present what that light will look like.

[/Quote']

Okay for our purpose here, let's assume that we are capable of detecting the entire EM spectrum. Rather, that we have a device that will translate any EM wave into something that we can detect (which is not a bad description of, say radio telescopes, as far as high level descriptions go...) My question is how light travel times will distort our perception of this hypothetical superluminal explosion (not worrying about the spectrum).

In my mind the only way that it could work would be if there was a luminal boom that behaved almost exactly like a shockwave from a sonic boom' date=' to my knowledge no one has ever worked on what a light shock wave would look like, so once again it seems like the only way to show that a superluminal object could exist would be to define real observables.[/quote']

You are still thinking within the confines of SR

My hypothesis is really that it is our perception of motion that obeys SR. This point is fairly obvious when we think about how SR derives the coordinate trasnformation, or how SR always talks of motion with respect to a given observer or frame of reference, or how each frame of reference has its own space and time. The perceptual effects include a time dilation and a length contraction quite similar to the one in SR. I know that in our current interpretation of SR, we think of it as applying to real space and time, independent of our perception. That is, we take out all the known light travel time effects, and the underlying space-time that remains is assumed to obey SR, even though it is inconsistent with the original derivation of SR. But if an object is moving superluminally (hypothetically, of course), there is no way you can take out the light travel time effects. This is the reason I kept asking if you could work backwards from the two perceived laser dots that there was only one underlying laser pointer. Or from the two phantom objects that there is only one object moving superluminally.

 

To make the answer short and to the point, yes, I'm suggesting that we consider the possibility that the luminal boom behaves exactly like a sonic boom. After all, there won't be a luminal boom to begin with if we take SR as applying to the underlying space and time (and accept the consequent relativistic Doppler shift formula.) BTW, the Doppler shift formula one would derive using arguments based on light travel time effects has a strikingly similar form as the relativistic version, demonstrating the similarity in their derivations.

[CPL.Luke]

the doppler shift formula is a consequence of an interaction between any inertial observer and a wave. SR or no. (just listen to a firetruck as it passes by)

 

in the case of a sonic boom, you can't define a frequency for the wave in question because it has ceased to be a standard sinusoidal sound wave and is now a shockwave (which has the interesting property of traveling faster than sound), you would have to quantify what an EM wave would look like in this event so that you could show that the phenomena would behave like the simplistic animation. Because at present there is no theoretical framework that would allow you to say that we could detect light coming off of a superluminal object.

[Mowgli]

the doppler shift formula is a consequence of an interaction between any inertial observer and a wave. SR or no. (just listen to a firetruck as it passes by)

Yes' date=' just that the relativisitic formula for it is different.

 

As the shockwave passes you, the frequency as you measure it is infinite. But immediately after the shockwave passes you, the frequency rapidly decreases. In my animation, the instant the luminal shockwave hits you is when you see the object at B'. As you see the phantoms move away from B', the observed frequencies move from gamma, x-ray, uv, visible all the way to RF. Since the angular position is a function of time, you can think of the frequency evolution in terms of the angle, which is what agrees well with the available data. So as for the luminal boom, true, you cannot measure the frequency of the shockwave, but immediately after the shockwave passes you, you can start measuring the frequencies. For the superluminal explosion, what I was suggesting though was, [i']ignore[/i] the frequencies altogether, and think of when the waves will reach you.

 

Did you say the shockwave travelled faster than sound? I didn't know that... Interesting. Why? Or, is it the footprint of the sonic boom that travels faster than sound?

[CPL.Luke]

http://en.wikipedia.org/wiki/Shock_wave

 

essentially a shockwave exists as a near instantaneous change in a medium, in other words the information about the event is transmitted very rapidly because the atoms in the medium become far closer to eachother than when a normal soundwave passes through the medium,

 

unfortunatly I can't give much more information than that as I am not an expert on shockwaves, however I do recall that the shockwave from a nuclear blast will travel at up to 3x the speed of sound.

[Mowgli]

I think I may be using the words luminal boom and shockwave with a different meaning in mind. I mean the conical wave front created by the waves emitted by object at different times overlapping, not the disruption of the medium created by the motion of the object. The picture in my 7th post in this thread illustrates what I mean.